Introducing Nonlinear Dynamics to Two-Regime Market Model: Theory and Evidence

Abstract

The existing two-regime asset pricing models do not reach a consensus, neither in the definition of bull and bear market conditions nor in modelling the non-stationarity of the beta. We propose a new logistic smooth transition regression model to address the beta non-stationarity issue. Using eight different definitions of bull and bear market conditions, we intend to ascertain the most appropriate definition with which to capture the non-linear dynamics of security returns. We find through a series of linearity tests that our model provides an adequate description of the data generating process. Further we explore the adequacy of a duration dependent description of market conditions in our model. Often we find that yield spread is a more appropriate definition of market condition than is a coincident economic indicator, excess market returns, and a moving average of excess market returns. We also find duration dependence in market conditions.